The Games and Puzzles Journal, #15 - Mayhematics

# GA*.{ES ANTD PLIZZLES J'LRNAL
Professor Cranium notes two points of
sociological or anthropological interest not
mentioned before: that it is from the Primitives
that rve get our sayings 'tea for two" and "beyond
our ksn" (meaning greater than fifteen).
Another of their sayings that has joined
the vsrnacular is "tet for tat" (meaning exchange
of one thing for something equal) this arises from
a further refinement to the Primitive sSrstem of
numerary nomenclafure in which the letter 'a'
indicates the operation of "raising to a po\,\'er".
Thus tat : Z? : 4 - ZxZ: tet.
This innovation allows some names to be
expressed moro concisely or by using lorver
numbers. The rule is followed that 'a' takes
priority ovsr 'e', thus tat is used for 4 in
preference to tet, and most number-names are
affected: I : tak, 9 : kat, 12 - tatek {i.e. ?2*3),
l3
since 42 : ?r), L7 : tatati, 18 : tekat, 19: tekati,
20 : taten, 24 : takek. 25 : nat, 26 : teltateki, 27
: kak, 28 : tated, 29 : tatedi, and so on.
Is this system free of ambiguities? If not
where do the first ambiguities occur? What is the
name of the number of the beast in this system?
Ansrver the same questions for another
tribe of primitives that use only t for 2 and k for
3, so that 5 - tati and 7 - teki.
2rg.Digitolryy
What is the smallest number which may
be divided into three different parts such that each
part multiplied by three gives the same digits in
the answer? with the right approach this is quite
easy
-
but with the \\nong approach ....
This is Problem 76, dated 20 April lg?3,
from T. R. Dalvson's manuscript book of
Original Puzzles (mentioned in issue 13, p .224).
ZL R Sncoher 9uesfion
In snooker. what is the maximum number
of breaks. all e+ual.,that can occur in a game if no
penalties are ar,varded?
For the uninitiated: there are 15 red balls
each scoring I point and six 'coloured' balls,
yellow, gresn, brown, blue, pink, black, valued at
2.,3,4,,5,6,7 points rsspectively. A r,vhite ball is
cued to knock the other balls into the pockets.
If a red is pocketed (potted) this permits a
colour to be potted on the next shot. (In snooker
red is not & colour, but black is!). The colour is
then replaced on the board (respotted) and another
red may be potted, followed by a colour, and so
on, until the last red has gone, and any colour
taken after the red has been respoffed. Then the
six colours must be potted in order of increasing
value. A break ends as soon as a pot is missed.
Thus, as is r,vell knonn svsn be5,'ond
snooker circles, the maximum score achievable in
a single break, by potting the 15 rsds, each
followed by the black, and then the six colours, is
(1 + 7)*15 + (7+3 + 4 +5 + 6 + 7l:147.
If the first player misses a pot the other
player takes over. Thus if the first player scores
72 by potting 9 reds and blacks, then &e second
player can win b,v scoring the remaining 75
points., or he can level the game by reaching 72,
say by potting three pinks instead of blacks after
the reds. This is the case of two equal breaks.
ZZ. ftrotfy
Draw the 21 different prime knots {p.250)
with I intersections, in the farm of King Tours,
using diagonal lines only for the intersections.
U3. Parsing the Port
This question is from Mr R. A. Watson.
Fifteen barrels of rvine were offered for sale,
containing the following numbers of gallons: 15.
16, 18, L9,71. 22, 23, 25,29, 3I,33, 34,37,39,
40. One barrel contained port, the others sherry.
Trvo merchants between them bought all the
shery. No-one bought the port. One merchant
bought trn'ice as many gallons of shery as the
other. No barrel was divided. Which barrel
contained the port?
?J*. X.O.If.s
This is another question from the
Original Puzzles manuscript by T. R. Darvson.
Problem numbet 1, dated 1914.
Four card plal'ers, playing for lorv and
variable stakes. havs made a practice of scribbling
I.O.U.s as the game proceeds, using them also as
coin tokens from deal to deal, settling up at the
close of play. After some pla,v one evening, they
held respectively the following papers: A, 2s, 5d,
Yrd; B, 9d, LYzd, C, ls, 3d; and D, 2s 6d, 6d. At
the close of the next hand the only payment \n'as
2d from B to A. Horv can it be affarrged without
writing out a fresh I.O.U.? [s - lzdl
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